Problem: $f(x)=(3x-5)^3$ $h(x)=2\sqrt[3]{x}+8$ Write $h(f(x))$ as an expression in terms of $x$. $h(f(x))=$
Let's write $f(x)$ as the input to function $h$. $h({f(x)})=2\sqrt[3]{{f(x)}}+8$ Since $f(x)=(3x-5)^3$, this becomes: $\begin{aligned} h({f(x)})&=2\sqrt[3]{{(3x-5)^3}}+8\\ \\ &=2(3x-5)+8\\ \\ &=6x-10+8\\ \\ &=6x-2 \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $h(f(x))=6x-2$